As we have already mentioned, our model, being BGL-like, ought to allow for an easy fit in the flavour sector, an assumption we now put to the test. In Fig. REF  we see how an agreement with \(b\rightarrow s\gamma \)  constraints is not automatic – in fact, we observe a number of (grey) points with larger than 2\(\sigma \)  deviation from the SM prediction, and quite a few disagreeing with the SM \(b\rightarrow s\gamma \)  values between 1 and 2\(\sigma \) . These larger than 1\(\sigma \)  deviations are seen to occur mostly (though not exclusively) for lower masses of the lightest charged scalar, \(m_{H_1}^\pm \le 700\)  GeV.
This is similar to what occurs for the Type II 2HDM [1]}.
Since in our model the down-type quark masses do not arise from a single \(\Gamma \)  matrix, it is in fact natural that we find regions of parameter space for which observables such as \(b\rightarrow s\gamma \)  behave in a similar manner to a Type II 2HDM. However, we see that our 3HDM can fit this observable for much lower charged Higgs masses than 700 GeV, as occurs, for instance in a Type I 2HDM – again to be expected, certain regions of our parameter space should mimic well the Type-I behaviour.
A similar phenomenon was observed for a 2HDM with tree-level FCNCs, see [2]}.
